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Ratio of ranges, heights or speeds of two projectiles at given angles

This type of question, asked 4 times: 26 Jul 2022, 8 Apr 2023, 10 Apr 2023, 4 Apr 2026 S1. All 6 questions below, oldest first.

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  1. Question 1

    26 Jul 2022

    19
    Two projectile thrown at 30∘30^{\circ} and 45∘45^{\circ} with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

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  2. Question 2

    26 Jul 2022

    91
    Two projectiles are thrown with same initial velocity making an angle of 45∘45^{\circ} and 30∘30^{\circ} with the horizontal respectively. The ratio of their respective ranges will be

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  3. Question 3

    8 Apr 2023

    2
    Two projectiles AA and BB are thrown with initial velocities of 40 m/s40\text{ }m/s and 60 m/s60\text{ }m/s at angles 30∘30^{\circ} and 60∘60^{\circ} with the horizontal respectively. The ratio of their ranges respectively is (g=10 m/s2)\left( g = 10\text{ }m/s^{2} \right)

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  4. Question 4

    10 Apr 2023

    4
    The range of the projectile projected at an angle of 15∘15^{\circ} with horizontal is 50 m50\text{ }m. If the projectile is projected with same velocity at an angle of 45∘45^{\circ} with horizontal, then its range will be:

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  5. Question 5

    10 Apr 2023

    107
    Two projectiles are projected at 30∘30^{\circ} and 60∘60^{\circ} with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

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  6. Question 6

    4 Apr 2026 S1

    6
    The two projectiles are projected with the same initial velocities at the 15∘15^{\circ} and 30∘30^{\circ} with respect to the horizontal. The ratio of their ranges is 1:x1:x. The value of xx is

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